German Published Patent Application No. 41 23 654 A1 describes a known method to prevent an unauthorized person from being able to use a transponder that has been forgotten in a vehicle to start the vehicle. In this known method, features are provided with which the vehicle is locked only if the transponder is definitely located outside the vehicle. Detection of the transponder position inside or outside the vehicle is accomplished with two antennas, of which one is directed toward the interior and the other toward the exterior. The fact that unlocking is possible only if the transponder signal arrives via the antenna directed toward the exterior ensures that the vehicle cannot easily be put into operation if the transponder was left inside the vehicle. Unauthorized starting of the vehicle is possible, however, if a transponder left behind in the vehicle comes into the possession of an unauthorized person via a break-in into the vehicle, and is used by that person. In addition, multiple authorized transponders are usually allocated to vehicles, so that even if care has been taken that the most recently used transponder is located outside the vehicle, it is possible for a further authorized transponder to be located in the vehicle; in the event of a break-in, it would then allow the vehicle to be started.